Author: Matthew Johantgen – Optical Engineer
Are you frustrated with your current AR/VR (XR) test setup? Are your headsets being inspected by people who give inconsistent results? Or are you stuck with an off-the-shelf conoscope that’s not delivering the promised performance? Perhaps you’re using a complete test system that comes with a less-than-optimal lens. If so, read on, because that’s why we exist.
We design and manufacture conoscopes that will help you become the go-to test engineer for your company. They give consistent results quickly. Their performance has no equal, and they are custom designed and manufactured for your leading edge headsets or glasses.
We are happy to work with your preferred test system manufacturer to give you the best results. Astigmatism compensation in AR/VR test lenses is a problem we’re actively thinking through. The industry hasn’t converged on a standard approach yet, and neither have we. If it’s a priority for your program, let’s talk about building it.
A lens for AR/VR testing must be designed so that its entrance pupil can be located within and scan the desired portion of the AR/VR device eyebox. The eyebox is different for all devices, but can be defined as the 3D volume that the user’s eye can move within and still view the image clearly. The mechanics of the conoscope must consider this volume and be designed accordingly.
The conoscope must also be designed to avoid any mechanical crashing with the AR/VR device mechanics. This often requires that the conoscope be designed in a periscope configuration (with a fold in the optical axis) to allow a sufficiently complex optical design, allowing for the needed aberration correction while avoiding mechanical crashing with the device.
The AR/VR device inter-pupillary distance (IPD) requirement significantly affects the size of the front of the conoscope; requiring that it be less than half of the minimum IPD needed. This can be difficult to achieve, especially for VR applications, because at wide angles, conoscopes want to become very large. When the conoscope can be made smaller than half the minimum IPD, it allows for 2 test systems to be used to simultaneously test both eyes at once.
First, we know that the Nyquist frequency of the sensor pixel is:
$$\nu_N = \frac{1000}{2 * P_x}$$
Where \( V_{\mathrm{N}} \) is the Nyquist frequency and Px is the pixel size in microns.
Since the GMAX3265 sensor has 3.2µm pixels, Nyquist is 156.25 cyc/mm.
The sensor also has a 37.36mm diagonal, so spreading 80° over this dimension gives us a ratio of 2.14 deg/mm. An angular frequency of 30 cyc/deg is then equivalent to a spatial frequency of 64.2 cyc/mm at the image. This is much less than Nyquist for the sensor so we have now determined that the camera will be able to resolve 30 cyc/deg.
So far this is a very good fit, but we also must consider the diffraction effects from the lens aperture. The cutoff frequency due to diffraction is determined by:
$$\nu_c = \frac{1}{\lambda \left( f / \# \right)}$$
This is the frequency at which the MTF goes to zero. For this example, using an EPD=5 and assuming imaging in the visible (λ=0.55µm) we get a cutoff frequency of about 340cyc/mm.
The table below shows this calculation in more detail (remember for an F-theta lens F = y’ / θ(radians), and the image space F/# = F / EPD)
As can be seen from the diffraction limited plot below, there is about 75% MTF at the required frequency (64.2 cyc/mm):
The conoscope specifications must result in a diffraction limit that exceeds the requirement at 30 cyc/deg, but it also must be designed with sufficient complexity to correct the aberrations to a level resulting in acceptable MTF at the desired frequency. Refer to this page to see what the effects of aberrations can have on the MTF.
Conoscopes designed for AR/VR inspection are often designed to work at multiple object distances. A conoscope capable of this is called a variable conjugate lens, varifocal, or variable object distance lens.
To inspect AR/VR devices the conoscope must be able to accommodate both near-sighted and far-sighted users. The conoscope must be able to “focus” to adjust for various object distances without changing the image size (i.e. 10° still maps to 10mm). This is the same requirement as “no breathing” in photography if you are familiar.
Most systems for this application cover object distances from 250mm in front of the lens to infinity. But some are capable of focusing from -100mm (i.e. inside the lens), to infinity, and to +100mm (i.e. in front of the lens). Optometrists speak in terms of Diopters, which have units of inverse meters. Zero Diopters (0D) correspond to an infinite object distance, and 10 Diopters (10D) corresponds to 0.1 meter, or 100mm. In these units, a normal system adjusts from 0D to 4D, whereas a wide range system ranges from -10D to +10D.
VR devices suffer much more from distortion than AR devices, because they require a much wider field of view. A lens designed for testing VR devices must be corrected for distortion and/or the distortion profile must be well known. This way, the conoscope can easily evaluate the VR device distortion without any confusion of where the distortion is coming from.
Our wide-field-of-view conoscopes are corrected for F-theta distortion so that the input angle is mapped directly to a distance on the image sensor for easy distortion calculations. See more on different distortion types here.
AR/VR headset manufacturers often ask us about measuring the distance to the virtual image (Virtual Image Distance or VID) produced by the headset. This is a very reasonable quality control request, but it runs into a basic geometrical optics constraint known as depth of field (DOF). DOF is the uncertainty in the VID measurement. Now let’s dive into the math.
The depth of field for a light cone is:
$$\mathrm{DOF}=\pm\,\mathrm{OPD}\,\cdot\,8\,\lambda\,(F/\#)^{2}$$
Where, OPD is the optical path difference due to defocus, λ is the wavelength and F/# is the object space F/# = VID / EPD.
So, the better you can measure the OPD due to defocus, the smaller the depth of field, or error in the VID.
If we use ¼ wavelength as the smallest detectable OPD defocus and a wavelength of 0.5µm (for visible light) the equation simplifies to:
$$\mathrm{DOF}=\pm\left(\frac{\mathrm{VID}}{\mathrm{EPD}}\right)^{2}$$ *units of microns, multiply by 0.001 to convert to mm
If we have a VID = 1.5m and an EPD = 3mm, we get:
DOF = ±0.001*(1500/3)^2 = ±250 mm.
This is often considered insufficient precision. The only way to increase the precision is to increase the EPD of the testing lens. Below is a table showing precision versus EPD.
This calculator will calculate the accuracy of a VID measurement based on the entrance pupil diameter (EPD) at the desired wavelength and VID. The VID measurement accuracy is equivalent to the Depth of field (DOF) calculated in the formula above.
For example, a 5 mm EPD conoscope lens at 0.50 µm wavelength with a 1500 mm VID yields a measurement accuracy of ±90 mm DOF.
This calculator will calculate the minimum entrance pupil diameter required to meet the desired VID measurement accuracy at the desired wavelength and VID. The VID measurement accuracy is equivalent to the Depth of field (DOF) calculated in the formula above.
For example, to achieve a measurement accuracy of ±90 mm DOF at 0.50 µm wavelength with a 1500 mm VID, a minimum entrance pupil diameter of 5.0 mm is required.
We have already designed and manufactured hundreds of conoscopes for display testing. Here are some examples of what our conoscopes have been used for:
If you are reading this page and found it useful, you may be interested in the following resources.
What can we do to meet your AR/VR/XR/MR testing needs? Let us know by filling our Contact Us form. We look forward to working with you.